On the geometric and topological rigidity of hyperbolic 3-manifolds
classification
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hyperbolicmanifoldconditiongeometricmanifoldsclosedequivalenceexamples
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A homotopy equivalence between a hyperbolic 3-manifold and a closed irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic manifold satisfies a purely geometric condition. There are no known examples of hyperbolic 3-manifolds which do not satisfy this condition.
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